Field effect transistors that use inorganic semiconductor materials are well known, being already manufactured as industrial products. Regarding the basic structure of such a field effect transistor, as shown in FIG. 4, the field effect transistor is arranged in a horizontal direction relative to a substrate 71. A source electrode layer 75 and a drain electrode layer 76 are provided separately from one another by an electrically neutral inorganic semiconductor layer (channel layer region) 74. A gate electrode 72 is disposed on the substrate 71, electrically isolated from the semiconductor layer 74 by a gate-insulating layer 73. The inorganic semiconductor layer 74 is formed of an inorganic material such as an inorganic amorphous material (hydrogenated amorphous Si) or an inorganic polycrystalline material is used as the inorganic semiconductor material constituting.
Moreover, thin film field effect transistors that use organic materials in the semiconductor layer are also well known. Regarding such conventional thin film field effect transistors that use organic materials, again many studies have been carried out into the ones having a basically similar structure to that of the thin film field effect transistor that uses an inorganic material described above, i.e. the ones that are arranged in the horizontal direction relative to the substrate 71. An organic material such as a π electron conjugated macromolecular compound or an aromatic compound has been used as the organic semiconductor material constituting the semiconductor layer 74, as described by A. Dodabalapur et al. in Appl. Phys. Lett., Vol. 69, pp. 4227-29 (December 1996).
With such thin film field effect transistors, an electric field applied from the gate electrode layer acts via the gate insulating layer on the semiconductor layer (channel part), thus controlling the current flowing between the source electrode layer and the drain electrode layer, whereby a transistor effect is realized. Thin film field effect transistors that use an organic material in the semiconductor layer have advantages compared with thin film field effect transistors that use an inorganic material such as Si in the semiconductor layer, namely:                the device can be manufactured without using a vacuum;        a uniform device having a large area can be manufactured;        the manufacturing method is simple, for example a plastic substrate can be used since the device may be manufactured using a low-temperature process.As a result of these, manufacturing cost can be reduced. However, there have been problems with thin film field effect transistors that use an organic material in the semiconductor layer compared with thin film field effect transistors that use an inorganic material such as Si in the semiconductor layer, for example:        a) the carrier mobility (which indicates the transistor performance) is low;        b) a large current cannot be passed; and        c) high-speed operation is not possible.        
As means for resolving these problems, hitherto it has been proposed to adopt a structure in which an organic material layer is disposed between a source electrode and a drain electrode, and the direction of current flow is made to be perpendicular to this organic material layer. For example, Yang et al. have proposed a device that uses a mesh of polyaniline as a gate electrode. More specifically, Yang et al. propose a “conducting network . . . the network is fractal with high surface area [which] functions as a high-performance electrode . . . the contact area for carrier injection into the polymer is increased . . . surface roughness . . . enhances the local electric field.” See Y Yang et al., Nature, Vol. 372, pp. 344 (1994). Fractals may be formed on a surface or in space. Frost on a windowpane is an example of a fractal on a surface. An example of a fractal is space is a “sponge,” for example, a cubical block measuring three units on a side, with a one-unit cubical void removed from the center of each face, followed by performing the same operation on each of the twenty-one remaining one-unit cubes, and so on infinitely.
Muraishi et al. have formed a gate electrode having nanoscale voids therein by using latex spheres as a vapor deposition mask when depositing the gate electrode, resulting in a gate electrode somewhat resembling Swiss cheese. See Muraishi et al., Technical Report of IEICE, OME2002-15 (2002-05) 13.
In addition, Japanese Patent Application Laid-open No. 2003-110 discloses a method of disposing a gate electrode on side walls of organic films.
In general, the thickness of an organic thin film can be reduced in thickness down to approximately 100 nm, whereas the precision of patterning in a direction parallel to a substrate is of the order of 100 μm. Consequently, if the direction of current flow is made to be perpendicular (vertical) to the organic thin film, then compared with the case that the direction of current flow is parallel (horizontal) to the organic thin film, the cross-sectional area of the current pathway will be larger (approximately 100 nm×100 μm→100 μm×100 μm), and the length of the current pathway will be shorter (approximately 100 μm→100 nm). Hence, the current density can be increased by several orders of magnitude.
However, there has been the following problem with the above. The range of the electric field applied from a gate electrode layer via a gate-insulating layer is generally limited to not more than 1 μm. Specifically, the range of the electric field is represented by the depletion layer thickness d, and is calculated from the following formula.d=(2εε0V/qNd)1/2 Here, Nd is the charge density, and is represented approximately by the following formula:Nd=Avogadro's number×impurity concentration×(1/molecular weight)×organic semiconductor material density.
For example, taking the permittivity ε of the organic semiconductor material to be 3, the gate voltage V to be 3V, the molecular weight to be 230, the impurity concentration to be 0.01%, and the organic semiconductor material density to be 2 g/cc, gives a charge density Nd of 5.1×1023 m−3, and a depletion layer thickness d of 44 nm. (Nd=Avogadro's number×impurity concentration×(1/molecular weight)×organic semiconductor material density=6×1023×0.0001×(1/230)×2×106=5.1×1023 m−3).
To control the current flowing between the source electrode layer and the drain electrode layer and thus realize transistor operation, it is necessary to make the spacing between the respective parts of the gate electrode less than this electric field range (i.e. less than 1 μm), but it is industrially difficult to form a gate electrode with such spacing. For example, if the gate resembles Swiss cheese then the hole diameter should be around 1022 m−3.
Moreover, if the proportion of the area of the device occupied by the gate electrode is high, then the area available for the current pathways will be limited. This will be disadvantageous in terms of the performance of the device.